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Pay-off diagrams are a way of depicting what an option or a set of options or options combined with other securities are worth at option expiration.

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What you do is you plot it based on the value of the underlying stock price.

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And I have two different plot types here. One that you might see more in an academic setting or a text book

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and one that you might see more if you look up pay-off diagrams on the internet or people actually trading options.

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But they are very similar. This one just worries about the actual value

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of the options at expiration. This worries about the profit and loss so this will incorporate what

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you paid for the option, this will not. This just says what it is worth. So with that said, we have company

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ABCD trading at $50 per share. Then we have a call option with a $50 strike price or $50 exercise price

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trading at $10 which tells us that the owner of that option has the rigth, but not the obligation, to

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buy company ABCD stock at $50 per share up to expiration, assuming it is an american option. If it was

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a european option it would be ON expiration. So what is the value of this option at expiration? So it's value at expiration, at expiration.

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So if the stock is worth less than $50, the owner wouldn't execute it. They wouldn't exercise the option so the option would be worthless, it would be worthless,

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they would just let it expire. No reason to actually exercise the option.

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Now if the underlying stock price is worth more than $50, if it is $51 then you would exercise it

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because now the option is worth one dollar, you can buy something for $50 and sell it for $51 so it is now worth

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one dollar. If the underlying stock price is $60 of course you would exercise it and now is worth $10 because you can buy something for 50 and you could immediately sell it at 60.

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We are saying that the underlying stock price is 60 so it would be worth 10. So you have a pay-off diagram

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that looks something like this. It kind of "hockey-sticks", below 50 it is worthless and then above 50

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all of a sudden it becomes worth something. Now if you do it in the profit and loss model, all you have

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to do is incorporate what you actually paid for the option. So in this situation, below $50 you still

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would not actually exercise your option because, why would you pay $50 for something that is actually

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trading for less than $50? But you would say, hey, I would have had to take a $10 dollar loss because

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I paid $10 for that option. So up until $50 your profit is negative 10. You have lost $10, you have lost the

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price of the option because you wouldn't exercise it. Then all of a sudden the stock price goes above

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$50 you would exercise it but you still have a negative profit because you still haven't made up the

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price of the option. All the way up until 60, at $60 per share for the underlying stock price you could

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exercise the option, buy the stock at 50, sell it at 60, you would make $10 doing that, but of course,

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you had to spend $10 on the option. So there you are break-even. But then you get as you get above

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a $60 stock price at maturity then all of a sudden you start to make money. So these are both legitimate

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pay-off diagrams for a call option, for this call option right over here.

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There are just different ways of doing it. This is the value of the option, this incorporates the actual cost of it.